The structural, mechanical and spectroscopic properties of boehmite (AlOOH polymorph) were investigated by means of first-principle density functional theory (DFT) and semiempirical density functional based tight binding (DFTB) methods. Apart from a marginal underestimation of interlayer hydrogen bond distances the DFT method well reproduces the experimental equilibrium low-pressure structure. For the DFTB method similar good agreement was obtained for lattice parameters, however bond lengths and angles showed a larger deviation from experiment in comparison to DFT results. The experimental spectrum of the OH stretching region was interpreted by means of the calculated frequencies within the frame of the harmonic approximation and by calculating the power spectra of the hydroxyl groups obtained from molecular dynamics simulations. Using the latter approach, the strong coupling between the individual OH modes was demonstrated. Isostatic structural compression of the boehmite structure was performed in order to obtain the bulk modulus and the dependence of the vibrational spectrum on the pressure. The DFT method gives a value of 97GPa in the athermal limit. Comparison with available bulk moduli for other AlOOH polymorphs reveals that boehmite shows the highest compression, for which mainly a strong shortening mechanism of interlayer hydrogen bonds is responsible. The DFT method also described correctly the dependence of the OH stretch frequencies upon compression resulting in a strong red shift. Although good performance is observed for the low-pressure region, the DFTB method is not found to be suitable for high-pressure studies in cases such as boehmite.